Question: Rewrite as a simplified fraction. ${0.4\overline{60} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 460.606...\\ 10x &= 4.606...\end{align*}}$ Subtracting the two equations, we have: ${990x = 456}$ ${x = \dfrac{456}{990}} $ ${x = \dfrac{76}{165}} $